Washington (CNN) -- The U.S. Army, already looking to shrink its force by 27,000 soldiers, is now also trying to cut more than 8,000 civilian jobs.

The plans call for the civilian jobs to be eliminated between now and October 2012, according to an Army official and a memo obtained by CNN.

The memo from Army Secretary John McHugh reads in part, "It is imperative that these reductions be accomplished as rapidly as possible, but no later than the end of FY 2012."

The cuts are part of the Army's plan to comply with the Secretary of Defense's instructions to return to fiscal year 2010 budget levels and keeping in line with the larger federal budget reduction efforts that predate the most recent national debt battle.

The Army, according to its website, has approximately 350,000 civilian employees.

The cuts would come through voluntary early separation or early retirement, attrition and, if necessary, layoffs.

Then-Defense Secretary Robert Gates said in January that the Army would cut its active-duty force by 27,000 soldiers as part of what Gates called "efficiency savings."

That reduction will take place beginning in 2015.

The Army's civilian job cuts may just be the beginning for the Pentagon. A senior Defense official said Wednesday that in the wake of the cuts spelled out in the debt reduction bill signed this week by President Barack Obama, thousands of civilians throughout the Defense Department may lose their jobs.